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Finding the Busier Street

Q: You routinely travel between A & B and have two streets you could drive through to get to B from A. There is a busy street that cuts through both streets so there are signals at X & Y (see fig). You are certain to be stopped at X and Y. Over a period of N days you want to ascertain which of the two routes is a busier one however as you drive you are in no position to count the number of vehicles in front of you and behind you. Assume you have no other data that you can collect other than what you can while driving your car. How do you find the busier street over a period of N days?

A: A surprisingly simple solution exists to find this. Take half the journeys \(\frac{N}{2}\) through route AXB and the other half through AYB. Simply keep track of the number of times you are stopped at the signal but are right in front of the queue facing the signal. This is easy to measure and count. In the less busier street you are more likely to be in front of the queue than the busier one!

Discovering Statistics Using R
This is a good book if you are new to statistics & probability while simultaneously getting started with a programming language. The book supports R and is written in a casual humorous way making it an easy read. Great for beginners. Some of the data on the companion website could be missing.

Linear Algebra (Dover Books on Mathematics)
An excellent book to own if you are looking to get into, or want to understand linear algebra. Please keep in mind that you need to have some basic mathematical background before you can use this book.

Linear Algebra Done Right (Undergraduate Texts in Mathematics)
A great book that exposes the method of proof as it used in Linear Algebra. This book is not for the beginner though. You do need some prior knowledge of the basics at least. It would be a good add-on to an existing course you are doing in Linear Algebra.

Follow @ProbabilityPuzIf you are looking to learn time series analysis, the following are some of the best books in time series analysis.

Introductory Time Series with R (Use R!)
This is good book to get one started on time series. A nice aspect of this book is that it has examples in R and some of the data is part of standard R packages which makes good introductory material for learning the R language too. That said this is not exactly a graduate level book, and some of the data links in the book may not be valid.

Econometrics
A great book if you are in an economics stream or want to get into it. The nice thing in the book is it tries to bring out a oneness in all the methods used. Econ majors need to be up-to speed on the grounding mathematics for time series analysis to use this book. Outside of those prerequisites, this is one of the best books on econometrics and time series analysis.